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→Properties
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=== Properties ===
=== Properties 属性 ===
In contrast to the conditional entropy for discrete random variables, the conditional differential entropy may be negative.
In contrast to the conditional entropy for discrete random variables, the conditional differential entropy may be negative.
与离散随机变量的条件熵相比，条件微分熵可能为负。
As in the discrete case there is a chain rule for differential entropy:
As in the discrete case there is a chain rule for differential entropy:
与离散情况一样，微分熵也有链式法则：
:<math>h(Y|X)\,=\,h(X,Y)-h(X)</math><ref name=cover1991 />{{rp|253}}
:<math>h(Y|X)\,=\,h(X,Y)-h(X)</math><ref name=cover1991 />{{rp|253}}
Notice however that this rule may not be true if the involved differential entropies do not exist or are infinite.
Notice however that this rule may not be true if the involved differential entropies do not exist or are infinite.
但是请注意，如果所涉及的微分熵不存在或无限，则此规则可能不成立。
Joint differential entropy is also used in the definition of the [[mutual information]] between continuous random variables:
Joint differential entropy is also used in the definition of the [[mutual information]] between continuous random variables:
联合微分熵也用于定义连续随机变量之间的共享信息：
:<math>\operatorname{I}(X,Y)=h(X)-h(X|Y)=h(Y)-h(Y|X)</math>
:<math>\operatorname{I}(X,Y)=h(X)-h(X|Y)=h(Y)-h(Y|X)</math>
<math>h(X|Y) \le h(X)</math> with equality if and only if <math>X</math> and <math>Y</math> are independent.<ref name=cover1991 />{{rp|253}}
<math>h(X|Y) \le h(X)</math> with equality if and only if <math>X</math> and <math>Y</math> are independent.<ref name=cover1991 />{{rp|253}}
当且仅当X和Y是独立的时，<math>h(X|Y) \le h(X)</math>才相等。
===Relation to estimator error===
===Relation to estimator error===